Srinagar District Magistrate Farooq Ahmad Lone said restrictions were imposed in the areas of Rainawari, Khanyar, Nowhatta, M.R. Gunj and Safa Kadal to maintain law and order.
Earlier, soldiers and a police special counter-insurgency force cordoned off Arwani village on a tip that armed militants were hiding in two homes, triggering a firefight, the officer said.
University of Kashmir has postponed all examinations scheduled to for today in view of the prevailing situation.
Yesterday, the joint separatist leadership called for complete shutdown in the Valley on Saturday against the killing of two civilians in firing by security forces.
A spokesman of the lawyers' body in a statement also condemned the firing on a passenger vehicle by army at Bandipora in which two civilians were critically injured.
Officials say dozens of youth have joined the rebel ranks since last July after a popular rebel leader was killed by security forces, sparking months of wide-scale protests in the territory. One of the two attacks took place in Hyderpora area of Srinagar where terrorists opened fire at a police party.